A Density Functional Theory (DFT) and Time-Dependent Density

May 4, 2007 - The PBE0 calculated resonant energy transfer rates are in a good agreement with the experimental rates and show the existence of many ...
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J. Phys. Chem. A 2007, 111, 4821-4828

4821

A Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT) Study on Optical Transitions in Oligo(p-phenylenevinylene)-Fullerene Dyads and the Applicability to Resonant Energy Transfer Teemu L. J. Toivonen* and Terttu I. Hukka Institute of Materials Chemistry, Tampere UniVersity of Technology, P.O. Box 541, 33101 Tampere, Finland ReceiVed: December 7, 2006; In Final Form: February 21, 2007

The optical transitions of three different size oligo(p-phenylenevinylene)-fullerene dyads (OPVn-MPC60; n ) 2-4) and of the corresponding separate molecules are studied using density functional theory (DFT) and time-dependent density functional theory. The DFT is used to determine the geometries and the electronic structures of the ground states. Transition energies and excited-state structures are obtained from the TDDFT calculations. Resonant energy transfer from OPVn to MPC60 is also studied and the Fermi golden rule is used, along with two simple models to describe the electronic coupling to calculate the energy transfer rates. The hybrid-type PBE0 functional is used with a split-valence basis set augmented with a polarization function (SV(P)) in calculations and the calculated results are compared to the corresponding experimental results. The calculated PBE0 spectra of the OPVn-MPC60 dyads correspond to the experimental spectra very well and are approximately sums of the absorption spectra of the separate OPVn and MPC60 molecules. Also, the absorption energies of OPVn and MPC60 and the emission energies of OPVn are predicted well with the PBE0 functional. The PBE0 calculated resonant energy transfer rates are in a good agreement with the experimental rates and show the existence of many possible pathways for energy transfer from the first excited singlet states of the OPVn molecules to the MPC60 molecule.

I. Introduction Organic conjugated materials are of great interest for application as active components in photovoltaic devices.1,2 Advantages of using organic materials in these devices are low cost, facile processing, thin size, and flexibility of properties and shape.3,4 On the other hand, organic materials require a good chemical stability and large optical absorption in the visible when they are used in photovoltaic devices.3 During the past decade the π-conjugated polymer-fullerene systems have gained much interest as electron donor-acceptor dyads when designing organic photovoltaic cells.5,6 A detailed understanding of the photoinduced charge transfer between a π-conjugated polymer and fullerene is required for further optimization of photovoltaic energy conversion. Time-resolved spectroscopy has revealed that photoinduced electron transfer in poly(p-phenylene-vinylene)-fullerene blends occurs in the femtosecond time domain.5,7-10 This is several orders of magnitude faster than any of the other decay processes and, therefore, the electron transfer has a high quantum efficiency.8,10 The back-electron transfer is orders of magnitude slower than the photoinduced forward electron transfer and the charge-separated state persists, even in the microsecond and millisecond time domains, which is essential for an efficient photovoltaic device.8 In solar cell structures designed from fullerene-containing polymers, the electron transfer is based on processes where the locally excited state of the conjugated polymer is formed first and the electron transfer to fullerene follows. However, the experimental results11,12 of oligo(p-phenylenevinylene) (OPVn) * Author to whom correspondence should be addressed. +358.3.3115.2108. E-mail address: [email protected].

Fax:

as a donor and N-methylfulleropyrrolidine, synthesized by Maggini et al.13 (MPC60), as an acceptor have revealed a twostep mechanism with an ultrafast resonant energy transfer (RET) from the photoexcited conjugated chain to the covalently linked fullerene derivative, followed by a picosecond time domain hole transfer from the MPC60 to the OPVn moiety. The experimental data shows that the electron transfer is much faster in films than in solutions and the RET can no longer be distinguished using the femtosecond pump-probe spectroscopy.12 In this paper, we use density functional theory (DFT) and time-dependent DFT (TDDFT) to study the optical transitions of the OPVn-MPC60 dyads (n ) 2-4) and of the separate OPVn and MPC60 molecules. The calculated transition energies are compared to each other and to experimental values, when available. Calculations are performed using the hybrid-type PBE0 functional. The RET from OPVn to MPC60 is studied by applying the Fermi golden rule with two different modelssthe point dipole model (PDM)14 and the extended dipole model (EDM)15sto describe the electronic coupling. The experimentally observed fast RET is explained based on the calculated results. The understanding of the RET and its importance as a step preceding the electron transfer is of great interest for the ability to control the energy flow in organic materials, which strongly impacts the efficiency of an organic device. In addition, by studying the energy transfer from oligomers with a varying number of monomers, information on the effect of the chain length and an estimation for more complex chains are obtained. The success of DFT and TDDFT in predicting the RET rates is also compared to corresponding semiempirical results obtained by Hukka et al.,16 who used semiempirical AM1 and INDO/ SCI methods to study the RET in oligo(p-phenylenevinylene)fullerene dyads. They showed that it is essential to go beyond

10.1021/jp068413v CCC: $37.00 © 2007 American Chemical Society Published on Web 05/04/2007

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Toivonen and Hukka

Figure 1. Molecular structure of OPVn-MPC60 (n ) 2-4).

TABLE 1. Energies (E) of HOMO, LUMO, and the HOMO-LUMO Gap of OPVn, MPC60, and OPVn-MPC60 Molecules, Calculated with the PBE0 Functional molecule

HOMO (eV)

LUMO (eV)

gap (eV)

OPV2-MPC60 OPV3-MPC60 OPV4-MPC60 OPV2 OPV3 OPV4 MPC60

-5.26 -4.97 -4.82 -5.13 -4.88 -4.75 -6.25

-3.37 -3.38 -3.37 -1.26 -1.69 -1.88 -3.49

1.89 1.59 1.45 3.87 3.19 2.87 2.76

the Fo¨rster model to obtain reliable estimates of the electron couplings mediating the energy-hopping process in these dyads.16 II. Theoretical Background and Methodology The molecular structure of the studied oligo(p-phenylenevinylene)-N-methylfulleropyrrolidine (OPVn-MPC60, n ) 2 4) is presented in Figure 1. First, the ground-state geometries and the electronic structures of the OPVn-MPC60 dyads and of the separate OPVn and MPC60 molecules were optimized using DFT.17-20 Next, TDDFT20,21 was used to calculate the electronic transition energies of these molecules. To obtain the fluorescence energies, the excited-state geometries of the OPVn units were optimized using TDDFT and the electronic transition energies were calculated using these geometries. Calculations were performed by the hybrid-type PerdewBurke-Ernzerhof exchange correlation functional (PBE0),22-26 in which the exchange functional is combined with the exact exchange functional from the Hartree-Fock theory (in a ratio of 25%). This functional was chosen because a previous computational study that was made by Pogantsch et al.27 shows that the hybrid-type PBE gives singlet transition energies for oligo(p-phenylenevinylenes) closest to the experimental values when compared to the hybrid-type B3LYP and the local density approximation (LDA) SVWN functionals. The significancy of the exact exchange functional included from the Hartree-Fock theory was determined by comparing the results given by the generalized gradient approximation-type exchange correlation functional (PBE)22-25 and PBE0. The PBE0 functional is shown to describe the experimental transition energies of the studied systems with much better accuracy than the PBE functional and, therefore, only the PBE0 results are presented in this article. The PBE results are presented in the Supporting Information. In TDDFT, the electronic excitations are calculated by starting from the ground-state Kohn-Sham (KS) orbitals and their eigenvalues.20 Thereafter, the electronic excitations are defined by means of the linear-response theory and using the adiabatic local density approximation (ALDA) for the functional derivatives of the exchange-correlation potential.20 Only singlet states have been considered. The Karlsruhe split-valence basis sets28,29 augmented with a polarization function (SV(P))30 were used in

Figure 2. (a) Highest occupied molecular orbital (HOMO) and (b) lowest unoccupied molecular orbital (LUMO) yielded by the PBE0 functional for OPV3-MPC60, OPV3, and MPC60. The isoamplitude surfaces of the orbitals presented are 10% of the maximum positive (red color) and minimum negative (blue color) values of the wavefunctions.

all calculations. The SV(P) basis set consists of one basis function for H (4s)/[2s] and six basis functions for C, N, and O (7s4p1d)/[3s2p1d]. All DFT and TDDFT calculations have been performed using the TURBOMOLE 5.8 software package.31,32 III. Results and Discussion Ground-State Electronic Structures of OPVn-MPC60, OPVn, and MPC60. The calculated energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies and the HOMO-LUMO gaps of the OPVn, MPC60, and the OPVn-MPC60 dyad molecules are presented in Table 1. These results indicate that the energy of HOMO of OPVn-MPC60 increases and the energy of LUMO of OPVn-MPC60 remains the same when the chain length of OPVn (i.e., the number of the PV monomers) increases. Comparing these values to the HOMO and LUMO energies of the separate OPVn and MPC60 molecules easily shows that the energy of HOMO of OPVn-MPC60 corresponds to the energy of HOMO of the separate OPVn molecule and the energy of LUMO of OPVn-MPC60 corresponds to the energy of LUMO of the separate MPC60 molecule. There are also other OPVn-MPC60 orbitals that have approximately the same energies as either an OPVn or MPC60 orbital. This means that the electronic structure of the OPVn-MPC60 dyad is approximately obtained by adding together the electronic structures of the separate OPVn and MPC60 molecules, as is also observed from Figure 2 where these orbitals are presented for the OPV3-MPC60 dyad and its separate counterparts (the same is true for the other OPVn-MPC60 dyads). As shown in Figure 2, the HOMO is delocalized over the entire p-phenylenevinylene chain of OPVn, because of the delocalization of the π-electrons.

Oligo(p-phenylenevinylene)-Fullerene Dyads

J. Phys. Chem. A, Vol. 111, No. 22, 2007 4823

Figure 4. Definitions of the reorganization energies λ0f1 and λ1f0. Figure 3. Energies (in electron volts) of (a) HOMOs and LUMOs, and (b) HOMO-LUMO gaps of OPVn and OPVn-MPC60 (n ) 2-4) molecules at their ground-state structures calculated with the PBE0 functional. The lines are the best linear fits to the orbital energies.

A small interaction between OPVn and MPC60 can be observed when the orbital energies of OPVn-MPC60 are compared to the orbital energies of the separate molecules, i.e., the energies of HOMO and LUMO of OPVn-MPC60 are ∼0.1 eV smaller and larger, respectively, than the corresponding orbital energies of the separate molecules. The HOMO-LUMO gaps of OPV2, OPV3, and OPV4 are 3.87, 3.19, and 2.87 eV, respectively. There is a clear dependence between the HOMO-LUMO gap energy and the OPV chain length; in other words, the gap energy decreases almost linearly as the chain length increases. This linear dependence of the HOMO-LUMO gap energy is presented in Figure 3 as the inverse of the number of the PV monomers, together with the energies of HOMO and LUMO. Linear dependence is also observed between the HOMO and LUMO energies and the inverse of the chain length (see Figure 3). The HOMO-LUMO gap energy of MPC60 is 2.76 eV, which is smaller than any of the OPVn gap energies. Therefore, when the excited state of OPVn is relaxed to its ground state, the energy liberated is higher than the gap energy of MPC60 and, therefore, an energy transfer from OPVn to MPC60 is expectable. Geometrical Structures of the OPVn Molecules at the Ground and Excited States and the Reorganization Energies. A reorganization energy λ describes the energy change of the molecule undergoing a structural change during an electronic transition when the molecule relaxes to its potential energy minimum of the new state. The larger the reorganization energy, the more the initial and final geometries differ. There are two reorganization energies for each OPVn, related to the transitions S0 f S1 and S1 f S0, which are presented in Figure 4. The first one (λ0f1) is related to the relaxation of an excited OPVn (i.e., OPVn*) to its excited-state potential energy minimum. The second one (λ1f0) is related to the relaxation of the OPVn after emission to its potential energy minimum at the ground state. These reorganization energies can be determined from the energies of the minima of the ground and excited states and the transition energies. Because, in this study, the reorganization energies are calculated for molecules under vacuum at a temperature of 0 K, the values describe only the internal

reorganization energies (i.e., the effect of solvent is not taken into account). The λ0f1 values are 0.18, 0.16, and 0.15 eV for OPV2, OPV3, and OPV4, respectively, and the λ1f0 values are 0.18, 0.15, and 0.14 eV for OPV2, OPV3, and OPV4, respectively. Because the reorganization energies are nonzero, the nuclear coordinates of the OPVn molecules, i.e., the groundstate and excited-state structures of OPVn differ from each other. The main structural differences are analyzed below. The difference between λ0f1 and λ1f0 describes the differences in the “steepnesses” of the ground-state and excited-state potential energy surfaces (molecular structures), which are very similar for all OPVn molecules. The sum of λ0f1 and λ1f0 describes the energy difference between the absorption and emission energies between the states at issue. The length of the double bond of vinylene in both the separate OPVn and OPVn of OPVn-MPC60 is 1.35 Å. The single-bond length of vinylene of the corresponding structures is 1.451.46 Å. The C-C bond lengths of phenylene are 1.39-1.42 Å at the ground state. At the excited state, the double bonds of vinylene are longer by 0.02-0.05 Å and the single bonds are shorter by 0.02-0.04 Å. At the excited state, the C-C bond lengths of phenylene changed -0.01-0.03 Å. The ethylbutoxyl side chains are tilted slightly, compared to their ground-state structures. Optical Transitions of OPVn and MPC60. The calculated S0 f S1 absorption and S1 f S0 emission energies of the OPVn molecules and the corresponding experimental values are presented in Table 2. All S0 f S1 transitions consist of oneelectron transitions mainly (∼90% or more) from HOMO to LUMO. The TDDFT results show a bathochromic shift both in the S0 f S1 absorption and in the S1 f S0 emission as the number of the repeating OPV monomers increases. The S0 f S1 transition energies are 3.36, 2.76, and 2.44 eV for OPV2, OPV3, and OPV4, respectively. These results are in a good agreement with the experimental values which are 3.47, 3.05, and 2.84 eV for OPV2, OPV3, and OPV4, respectively, in chloroform at room temperature.33 The longer the OPVn chain, the more the calculated transition energies differ from the corresponding experimental values. The S1 f S0 transition energies are 3.00, 2.45, and 2.15 eV for OPV2, OPV3, and OPV4, respectively. These results are in a very good agreement with the experimental values, which are 3.03, 2.66, and 2.47 eV for OPV2, OPV3, and OPV4, respectively, in chloroform at room

4824 J. Phys. Chem. A, Vol. 111, No. 22, 2007

Toivonen and Hukka

TABLE 2. Absorption and the Fluorescence Energies, and the Oscillator Strengths of OPVn and MPC60, Calculated Using the TDDFT/PBE0, and the Corresponding Experimental Values S0 f S1

S1 f S0

calculated molecule OPV2 OPV3 OPV4 MPC60 a

calculated

transition energy

oscillator strength

experiment

transition energy

oscillator strength

experiment

3.36 2.76 2.44 1.95

0.72 1.56 2.34 0.002

3.47a 3.05a 2.84a

3.00 2.45 2.15

0.80 1.71 2.55

3.03a 2.66a 2.47a

b

Experimental values are obtained in chloroform, from ref 33. b See experimental spectra in refs 13 and 38.

Figure 5. TDDFT/PBE0 calculated and the experimental OPVn (n ) 2-4) S0 f S1 absorption and S1 f S0 emission energies, as a function of the inverse of the chain length (n) of the OPVn. The lines are the best linear fits to the transition energies.

temperature.33 In the case of absorption and also in the case of fluorescence, the energy decreases when the chain length increases. The dependence of the S0 f S1 and S1 f S0 transition energies on the chain length of OPVn is illustrated in Figure 5. There is a clear linear dependence between the transition energy and the inverse of the OPVn chain length, and this linear dependence of the transition energies on the inverse of the chain length has been established earlier experimentally as well as theoretically.27,33-35 TDDFT results do not predict the dependence of the transition energy on the OPVn chain length totally correctly. This is attributed to the use of ALDA for the functional derivatives of the exchange-correlation potential but not to the optimization of the geometry.27 ALDA underestimates the excitation energies in the case of π-conjugated oligomers.36,37 We also calculated the transition energies for the PBE-optimized OPVn structures, using the PBE0 functional. These results differ from the PBE0 results only by ∼0.1 eV, meaning that the weakness of the PBE functional to predict the transition energies is mainly due to the inability to predict transition energies, not due to the inability of the PBE to predict structures. The calculated MPC60 absorption spectrum shows peaks at 1.8, 2.8, and 3.3 eV and shoulders at 2.4-2.5 eV and at 3.8 eV (see Figure 6). The overall shape, as well as the characteristic energies, correspond to the experimental values13,38 extremely well. At this point, for the energy transfer calculations presented later, it is worth noticing that the large amount of transitions in a wide energy range forming absorption of MPC60. The absorption spectra simulated in the range of 1-4 eV for OPVn and MPC60 are presented in Figure 6. In the spectra, the transition energies and the corresponding oscillator strengths are plotted using a Gaussian distribution function with a standard deviation of 0.10 eV. Absorption Spectra of OPVn-MPC60. As noted previously, the electronic structure of OPVn-MPC60 is approximately obtained by adding the electronic structures of the separate OPVn and MPC60 molecules together and no significant interaction

Figure 6. Absorption spectra of OPVn (n ) 2-4) and MPC60 calculated using the TDDFT/PBE0. Circles present the calculated transition energies and oscillator strengths of different transitions.

between OPVn and MPC60 exists. Therefore, the absorption spectrum of OPVn-MPC60 should be similar to the spectrum formed by adding the spectra of OPVn and MPC60 together. The calculated spectra are presented in Figure 7. Unfortunately, because of the high computational cost of the absorption energy calculations of OPVn-MPC60, only the absorption energies up to ∼3.2-4.0 eV were achieved within the available computational time. Fortunately, these energies are high enough to allow a comparison with some of the lowest excited states of MPC60 and OPVn. Based on the calculated results, one can make a conclusion that the absorption spectra of OPVn-MPC60 are approximate sums of the absorption spectra of OPVn and MPC60, as expected. The absorption spectra of OPVn-MPC60 are redshifted by ∼0.1 eV, compared to the sum spectra of OPVn and MPC60, which is due to small interactions between OPVn and MPC60, as discussed previously. The similarity of the shapes of the OPVn-MPC60 spectra and the sum spectra of OPVn and MPC60 is also observed in the experimental spectra.38 TDDFT shows that there is interaction between the OPVn and C60 molecules at the ground state, because, in the absorption spectra

Oligo(p-phenylenevinylene)-Fullerene Dyads

J. Phys. Chem. A, Vol. 111, No. 22, 2007 4825 rule) in the weak coupling approximation:42

kiD-jA )

2π 2 J V p iD-jA iD-jA

(2)

The traditional method for calculating the electronic coupling term, ViD-jA, was developed by Fo¨rster (the point dipole model (PDM))14 and is presented as

ViD-jA )

κiD-jA|µiD||µjA|

(3)

3 4π0RD-A

where |µiD| and |µjA| are the magnitudes of the transition dipoles of the donor and the acceptor and RD-A is the distance between the centers of the chromophores. The term κiD-jA is the orientation factor between the transition dipoles and is defined as

κiD-jA )µ biD‚µ bjA - 3(µ biD‚R BD-A)(µ bjA‚R BD-A)

Figure 7. (s) Absorption spectra of OPVn-MPC60 (n ) 2-4) and (- - -) the sum spectra of OPVn (n ) 2-4) and MPC60 simulated on the basis of the transition energies of different transitions calculated using the TDDFT/PBE0.

of OPVn-MPC60, there are extra transitions at energies of ∼1.3-1.7 eV if compared to the sum spectra of OPVn and MPC60. In these transitions, charge is transferred from the OPVn molecule to the MPC60 molecule and charge transfer states are formed. It is well-known that TDDFT does not predict excitation energies of charge-transfer excited states perfectly. This is due to the failure of exchange-correlation potentials to decay faster than the correct 1/r asymptotic decay, where r is the electronnuclear distance.39-41 These types of excited-state transitions are not discussed in the context of the experimental results. That might be due to the low energies and the low absorbances of these transitions, which make them difficult or even impossible to observe in the UV-vis spectra. Theory and Results of the Resonant Energy Transfer Rate Calculations. To calculate the RET from the excited OPVn (OPVn*) to MPC60, the structures of the OPVn*-MPC60 systems were built by replacing OPVn with the OPVn* excited-state geometry in the OPVn-MPC60 ground-state structure. In the weak coupling regime, RET occurs from a geometrically fully relaxed donor.16 The RET is supposed to happen intramolecularly from the locally excited donor (OPVn*) to MPC60, so charge-transfer transitions are not considered. On the basis of the excited-state fluorescence and the groundstate absorption properties provided by TDDFT, the total rate for the RET from an oligo(p-phenylenevinylene) to the fullerene derivative was calculated by summing the hopping rates over all acceptor states:

kRET )

ki -j ∑ j D

A

(1)

A

where iD denotes the lowest donor excited state (of OPVn) that is involved in the donor emission and jA runs over all acceptor excited states (of MPC60) located within a 1-4 eV span from the ground state (such a large spectral range grasps all acceptor states with a significant spectral overlap with the donor emission and ensures a full convergence of the results). Each term in the summation corresponds to a pathway for energy migration and contributes to a partial rate given by eq 2 (the Fermi golden

(4)

The Fo¨rster’s PDM is known to fail in producing accurate couplings when the distance between the chromophores is short, compared to their planar dimensions,43 as is the case in this study. This was also observed experimentally for OPV4-MPC60 in a toluene solution11 as well as with semiempirical methods.16 Therefore, different models have been developed to describe the electronic coupling between molecules with a short intermolecular distance and for taking into account the threedimensional structure of the transition density. Other models include, for example, the extended dipole model (EDM)15 and atomic transition density model (ATDM),16,42 as well as the transition density cube method,44 which take the chemical structure and the topology of the interacting chromophores into account and thereby produce more-reliable couplings. Because the transition densities are not available from the current version of the software used, the EDM is used in addition to PDM to define the electronic couplings between the interacting chromophores of the studied molecules. In the extended dipole model, the donor (acceptor) is replaced by the dipoles of the two opposite charges +qiD (+qjA) and -qiD (-qjA) at a distance of |lBiD| (|lBjA|). The dipole is assumed to have a value and a direction of the transition moment b µiD (µ bjA), i.e.,

b µ iD ) qiDBl iD

(5a)

b µ jA ) qjABl jA

(5b)

and

The |lBiD| and |lBjA| are generally chosen to be on the order of the size of the chromophores. In the case of OPVn, distances between the center points of the outermost phenyl rings, i.e., 6.6, 13.2, and 19.8 Å, were chosen for the lD values for OPV2, OPV3, and OPV4, respectively. The lA value of MPC60 is 7.3 Å, which corresponds approximately to the diameter of the C60 fragment, because the transition densities of MPC60 are mainly located on C60.16 The electronic coupling term, ViD-jA (expressed in units of cm-1), for different channels in eq 2, according to the EDM, is defined as follows:

ViD-jA )

(

qiDqjA

)

1 1 1 1 + 4π0 a1,iD-jA a2,iD-jA a3,iD-jA a4,iD-jA

(6)

where qiD (qjA) is the charge of the donor (acceptor) obtained

4826 J. Phys. Chem. A, Vol. 111, No. 22, 2007

Toivonen and Hukka and electronically excited states. In a hypothetical case of displacing the quadratic potential energy surfaces along one single normal mode, the probability for the 0-ν vibrational transition at 0 K is given by the square of the vibronic coupling term, i.e., the Franck-Condon factor (FCF):48

FCF0-υ )

Figure 8. Definition of the parameters of the two dipoles used to calculate the electronic couplings.

from formula3 for the excited state i (j). Distances ak,iD-jA (k ) 1, 2, 3, 4) represent the distances between the charges (qiD ((qjA) and are presented in Figure 8. The orientation of the distance BliD (lBjA)was set to be the same as the orientation of the transition dipole moment b µiD (µ bjA). The EDM is known to be a good approximation for strongly allowed transitions for molecules where the separation of chromophores is small, compared to their planar dimensions, and less good for weakly allowed transitions.45 The EDM has been originally used to describe an electronic coupling of dye molecules in aggregates;15 however, in this study, it is applied to defining coupling between two molecules of different types. For all OPVn molecules, the S1 f S0 transition is strongly allowed (the transition dipole moments are ∼10 D); however, for MPC60, most of the S0 f Sn transitions are weakly allowed (the transition dipole moments are 3.0 eV. The emission spectrum of OPV2 overlaps with a widest range of the excited states of MPC60, whereas the emission spectra of OPV3 and OPV4 overlap with much fewer MPC60 excited states, as seen in Figure 9. This means that there are more possible energy-transfer channels from OPV2 than from OPV3 or OPV4 to MPC60. Together with the electronic couplings, this also effects the energy-transfer rate and makes it the fastest for OPV2-MPC60. Overall, the energy transferred from an excited OPVn molecule can excite the MPC60 to many different excited states, inducing a fast RET. IV. Conclusions We have studied the ability of density functional theory (DFT) and time-dependent density functional theory (TDDFT) to predict the optical transitions of the OPVn-MPC60 (n ) 2-4) dyad and the separate OPVn and MPC60 molecules with the hybrid type PBE0 functional. The calculated S0 f S1 transition energies of OPVn are only 0.1-0.4 eV smaller than the experimental energies. The calculated energies of the first excited-state emissions of different OPVn are in good agreement with the experimental values, although all calculations predict

a stronger bathocromic shift for OPVn fluorescence than found in the experiments. For the S1 f S0 transition, the calculated energies are 0-0.3 eV smaller than the experimental energies. The longer the OPVn chain length, the more the calculated transition energies differ from the experimental values. The calculations predict the overall shape and the characteristic energies of the MPC60 absorption spectrum very well. The calculated absorption spectra of OPVn-MPC60 are observed to be approximately the sums of the absorption spectra of the separate OPVn and MPC60 molecules, as is the case with the experimental spectra. Calculations reveal a low-intensity band near the infrared region, which is attributed to a charge-transfer state that is not seen in the experiments. We have also used the extended dipole model (EDM) together with the results of the TDDFT description of the electronic excitations to study the resonant energy transfer (RET) in the OPVn-MPC60 dyads. The RET rates calculated from the TDDFT/PBE0 transitions using the EDM are comparable to the experimental values, taking into account the crudeness of the EDM used. The calculated kRET values are 1.5, 0.7, and 0.2 ps-1 for OPV2-MPC60, OPV3-MPC60, and OPV4-MPC60, respectively. The fast RET rates observed for OPVn-MPC60 molecules can be explained by the high number of possible MPC60 excited states absorbing the energy from the excited OPVn. The amount of absorbing states of MPC60 that overlap with the emission spectra of OPVn is the highest for OPV2, whereas the emission spectra of OPV3 and OPV4 overlap with much fewer of the MPC60 excited states. Therefore, more possible energy-transfer channels exist from OPV2 than from OPV3 or OPV4 to MPC60, and, together with the electronic couplings, this causes the energy-transfer rate to be the fastest for OPV2-MPC60. Acknowledgment. The authors acknowledge helpful discussions with Dr. D. Beljonne (University of Mons-Hainaut and Georgia Institute of Technology), Prof. J.-L. Bre´das (Georgia Institute of Technology and University of Mons-Hainaut), and Prof. T. T. Rantala (Tampere University of Technology). Prof. H. Lemmetyinen, the head of the Institute of Materials Chemistry at Tampere University of Technology, is acknowledged for offering the facilities for this research. The work is supported by the Academy of Finland. The computations presented in this document have been made with the CSC’s computing environment. (CSC is the Finnish IT Center for Science and is owned by the Ministry of Education.) T.L.J.T. also thanks the Emil Aaltonen Foundation, Tampere, Finland, for a traveling allowance to visit at the Georgia Institute of Technology. T.I.H. also thanks the Georgia Institute of Technology for a research fellowship.

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